Question

Solve $\frac{57}{x+y}+\frac{6}{x-y}=5;\frac{38}{x+y}+\frac{21}{x-y}=9$

Answer 1

$\frac{57}{x+y}+\frac{6}{x-y}=5$ __ (i) & $\frac{38}{x+y}+\frac{21}{x-y}=9$ __ (ii)

let, $\frac{1}{x+y}=A$

$\frac{1}{x-y}=B$

$57.A+6B=5$ _ _ _ (iii) $\times 21$

$38.A+21.B=9$ _ _ _ (iv) $\times 6$

$\to$ slove equation (iii) & (iv)

$1197.A+126B=105$

$\therefore 228.A+126B=54$

____________________

$969.A=51$

$A=\frac{51}{969}$

$A=\frac{3}{57}$

$\to$ Put value of A in equation (iii)

$57\times \frac{3}{57}+6B=5$

$3+6B=5$

$6B=2$

$B=1/3$

$\to A=\frac{3}{57}=\frac{1}{x+y}$

$\therefore 3(x+y)=57$

$\therefore x+y=57/3$ __ (v)

$\to B=\frac{1}{3}=\frac{1}{x-y}$

$\therefore x-y=3$ _ _ _ (vi)

solve equation v & vi

$x+y=57/3$

$x-y=3$

____________

$2x=\frac{57}{3}+3$

$2x=\frac{66}{3}$

$x=\frac{66}{6}=11$

put value of x in equation (vi)

$11-y=3$

$y=11-3$

$y=8$